Lattice integrals of motion of the Ising model on the cylinder

We consider the 2D critical Ising model with spatially periodic boundary conditions. It is shown that for a suitable reparameterization of the known Boltzmann weights the transfer matrix becomes a polynomial in the variable csc(4u)$csc\left(4u\right)$, u$u$ being the spectral parameter. The coefficients of this polynomial are decomposed on the periodic Temperley–Lieb algebra by introducing a lattice version of the local integrals of motion.     

Competition between Abelian and Zeeman magnetic field effects in a two dimensional ultracold gas of fermions

The ground state of ultracold fermions in the presence of effects of orbital and Zeeman magnetic fields is analyzed. Five different states are found: unpolarized superconducting state, partially and fully polarized normal states and phase separated regions, partially or fully polarized. The system, in the presence of orbital synthetic magnetic field effects, shows non-monotonous changes of the phase boundaries when electron concentration is varied. We observe not only reentrant phenomena, but also density dependent oscillations of different areas of the phase diagram. Moreover the chemical potential shows oscillatory behavior and discontinuities with respect to changes in the number of fermions.     

Lattice density functional theory for confined Ising fluids: comparison between different functional approximations in slit pore

ABSTRACT

In this paper, Lafuente and Cuesta's cluster density functional theory (CDFT) and lattice mean field approximation (LMFA) are formulated and compared within the framework of lattice density functional theory (LDFT). As a comparison, an LDFT based on our previous work on nonrandom correction to LMFA is also developed, where local density approximation is adopted on the correction. The numerical results of density distributions of an Ising fluid confined in a slit pore obtained from Monte Carlo simulation are used to check these functional approximations. Due to rational treatment on the coupling between site-excluding entropic effect and contact-attracting enthalpic effect by CDFT with Bethe-Peierls approximation (named as BPA-CDFT for short), the improvement of BPA-CDFT beyond LMFA is checked as expected. And it is interesting that our LDFT has a comparative accuracy with BPA-CDFT. Apparent differences between the profiles such as solvation force, excess adsorption quantity and interfacial tension from LMFA and non-LMFAs are found in our calculations. We also discuss some possible theoretical extensions of BPA-CDFT.     

Thermodynamic Foundations of Kinetic Theory and Lattice Boltzmann Models for Multiphase Flows

This paper demonstrates that thermodynamically consistent lattice Boltzmann models for single-component multiphase flows can be derived from a kinetic equation using both Enskog's theory for dense fluids and mean-field theory for long-range molecular interaction. The lattice Boltzmann models derived this way satisfy the correct mass, momentum, and energy conservation equations. All the thermodynamic variables in these LBM models are consistent. The strengths and weaknesses of previous lattice Boltzmann multiphase models are analyzed.     

A No-Go Theorem for Compatibility Between Involutions of First Order Differentials on a Lattice and Continuum Limit

We prove that the following three properties cannot match each other on a lattice, that differentials of coordinate functions are algebraically dependent on their involutive conjugates, that the involution on a lattice is an antihomomorphism, and that differential calculus has a natural continuum limit.     

Some characteristic behavior of mixed spin-1/2 and spin-1 Ising nano-tube

The magnetization of a cylindrical Ising nano-tube is investigated by the use of the effective field theory with correlations. The effects of the crystal field couplings at the surface shell to the order parameters, susceptibility, internal energy, specific heat and free energy are investigated. Some characteristic phenomena are examined in the thermal variations, depending on crystal field term. Moreover, tricritical and critical points are found on the (D/J,kT/J) plane, where D/J and kT/J are reduced crystal-field and temperature, respectively.     

3维U(1)改进格点规范理论中胶球质量和胶球波函数

用改进的格点规范场哈密顿量和截断本征方程法计算2+1维U(1)规范场的胶球质量(质量隙)和胶球波函数,结果显示出较好的标度行为.     

Monte Carlo simulations of conformal theory predictions for the three-state Potts model

The critical properties of the three-state Potts model are investigated using Monte Carlo simulations. Special interest is given to the measurement of three-point correlation functions and associated universal objects, i.e., structure constants. The results agree well with predictions coming from conformal field theory, confirming, for this example, the correctness of the Coulomb gas formalism and the bootstrap method.     

集团蒙特卡罗方法对一维量子X－Y模型的研究

本文用一种集团Ｍｏｎｔｅ－Ｃａｒｌｏ模拟方法对一维量子Ｘ－Ｙ模型作了研究。在Ｌ＝３２、６４和１２８的自旋点阵上和βＪ＝１．０—１０．０的温度区域内，仔细分析了该方法的动力学性质，给出了相应的热力学量的模拟计算结果。该方法可以发展应用于格点费米子系统。     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models

We study the chromatic polynomial P_G(q) for m× n square- and triangular-lattice strips of widths 2≤ m ≤ 8 with cyclic boundary conditions. This polynomial gives the zero-temperature limit of the partition function for the antiferromagnetic q-state Potts model defined on the lattice G. We show how to construct the transfer matrix in the Fortuin–Kasteleyn representation for such lattices and obtain the accumulation sets of chromatic zeros in the complex q-plane in the limit n→∞. We find that the different phases that appear in this model can be characterized by a topological parameter. We also compute the bulk and surface free energies and the central charge.     

An optional explanation for nickel sites of nickel-zinc phosphate glasses by their optical spectra and EPR g factor

In this paper, the nickel site, optical spectra and electron paramagnetic resonance (EPR) g factor of nickel-zinc phosphate glasses have been studied by ligand-field theory. The orbital mixing effect between p and d orbits has been included in the calculation by two-spin-orbit parameter model. The present study shows that nickel occupies the tetrahedral zinc site with cubic symmetry in nickel-zinc phosphate glasses. Unlike the result of previous study that assigns nickel to an octahedral interstitial site, it is an optional explanation for nickel sites in nickel-zinc phosphate glasses by analysing the optical absorption spectra and EPR g factor.     

Ferromagnetism in the periodic Anderson model. A comparison of spectral density approximation (SDA), modified alloy analogy (MAA) and modified perturbation theory (MPT)

We compare different approximation schemes for investigating ferromagnetism in the periodic Anderson model. The use of several approximations allows for a detailed analysis of the implications of the respective methods, and also of the mechanisms driving the ferromagnetic transition. For the Kondo limit, our results confirm a previously proposed mechanism leading to ferromagnetic order, namely an RKKY exchange mediated via the formation of Kondo screening clouds in the conduction band. The contrary case is found in the intermediate-valence regime. Here, the bandshift correction ensuring a correct high-energy expansion of the self-energy is essential. Inclusion of damping effects reduces stability of the ferromagnetic phase. Received 5 June 2000 and Received in final form 3 August 2000     

Dynamic magnetic hysteresis behavior and dynamic phase transition in the spin-1 Blume-Capel model

The nature (time variation) of response magnetization m(wt) of the spin-1 Blume-Capel model in the presence of a periodically varying external magnetic field h(wt) is studied by employing the effective-field theory (EFT) with correlations as well as the Glauber-type stochastic dynamics. We determine the time variations of m(wt) and h(wt) for various temperatures, and investigate the dynamic magnetic hysteresis behavior. We also investigate the temperature dependence of the dynamic magnetization, hysteresis loop area and correlation near the transition point in order to characterize the nature (first- or second-order) of the dynamic transitions as well as obtain the dynamic phase transition temperatures. The hysteresis loops are obtained for different reduced temperatures and we find that the areas of the loops are decreasing with the increasing of the reduced temperatures. We also present the dynamic phase diagrams and compare the results of the EFT with the results of the dynamic mean-field approximation. The phase diagrams exhibit many dynamic critical points, such as tricritical (•), zero-temperature critical (Z), triple (TP) and multicritical (A) points. According to values of Hamiltonian parameters, besides the paramagnetic (P), ferromagnetic (F) fundamental phases, one coexistence or mixed phase region, (F+P) and the reentrant behavior exist in the system. The results are in good agreement with some experimental and theoretical results.     

Image systems for the reaction field inside spheroidal dielectric objects and applications

Charges inside a dielectric object embedded in a dissimilar dielectric medium polarize the surrounding medium, which in turn makes a contribution, called the reaction field, to the electric field inside the object. In this work, we develop complete image systems for the reaction field inside a prolate or oblate spheroidal dielectric object embedded in an infinite dissimilar dielectric medium. In either case, an image system consists of a point image and a symmetric surface image over an exterior confocal spheroid that passes through the point image. As an application, the point image is applied into the generalized image charge solvation model (GICSM) and is tested in simulations of liquid water, and the results are analyzed in comparison with those obtained from the ICSM simulation as references. The results indicate that, for both the prolate and oblate cases, the single point image charge approximation for the reaction field inside the dielectric cavity of the model is good enough for the GICSM to faithfully reproduce typical static and dynamic properties of the liquid water at least when the spheroidal cavity has relatively small eccentricity.     

Optimised Dirac operators on the lattice: construction,properties and applications

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross‐Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so‐called overlap‐hypercube fermions in the two‐flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p‐regime and in the ϵ‐regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian – the chiral condensate and the pion decay constant – from QCD simulations with extremely light quarks.